## A law of iterated logarithm for stationary Gaussian processes.(English)Zbl 0273.60016

### MSC:

 60F10 Large deviations 60F20 Zero-one laws 60G10 Stationary stochastic processes 60G17 Sample path properties 60G15 Gaussian processes
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### References:

 [1] W. Feller, The fundamental limit theorems in probability, Bull. Amer. Math. Soc. 51 (1945), 800 – 832. · Zbl 0060.28702 [2] W. Feller, The general form of the so-called law of the iterated logarithm, Trans. Amer. Math. Soc. 54 (1943), 373 – 402. · Zbl 0063.08417 [3] Pramod K. Pathak and Clifford Qualls, A law of iterated logarithm for stationary Gaussian processes, Trans. Amer. Math. Soc. 181 (1973), 185 – 193. · Zbl 0273.60016 [4] James Pickands III, An iterated logarithm law for the maximum in a stationary Gaussian sequence, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 12 (1969), 344 – 353. · Zbl 0181.20703 [5] James Pickands III, Upcrossing probabilities for stationary Gaussian processes, Trans. Amer. Math. Soc. 145 (1969), 51 – 73. · Zbl 0206.18802 [6] James Pickands III, Asymptotic properties of the maximum in a stationary Gaussian process., Trans. Amer. Math. Soc. 145 (1969), 75 – 86. · Zbl 0206.18901 [7] Clifford Qualls and Hisao Watanabe, An asymptotic 0-1 behavior of Gaussian processes, Ann. Math. Statist. 42 (1971), 2029 – 2035. · Zbl 0239.60031 [8] Clifford Qualls and Hisao Watanabe, Asymptotic properties of Gaussian processes, Ann. Math. Statist. 43 (1972), 580 – 596. · Zbl 0247.60031 [9] C. Qualls, G. Simmons and H. Watanabe, A note on a $$0-1$$ law for stationary Gaussian processes, Mimeo Series #798, Inst. of Statistics, University of North Carolina, Raleigh, N. C., 1972. [10] Clifford Qualls and Hisao Watanabe, Asymptotic properties of Gaussian random fields, Trans. Amer. Math. Soc. 177 (1973), 155 – 171. · Zbl 0274.60030 [11] Hisao Watanabe, An asymptotic property of Gaussian processes. I, Trans. Amer. Math. Soc. 148 (1970), 233 – 248. · Zbl 0214.16502 [12] Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. · Zbl 0011.01703
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